Normally ζ-reversible profinite groups
We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally ζ-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155198 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Normally ζ-reversible profinite groups / L. Cimetta, A. Lucchini // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 24-50. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862615314962841600 |
|---|---|
| author | Cimetta, L. Lucchini, A. |
| author_facet | Cimetta, L. Lucchini, A. |
| citation_txt | Normally ζ-reversible profinite groups / L. Cimetta, A. Lucchini // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 24-50. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally ζ-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if G is a normally ζ-reversible satisfying one of the following properties: G is prosoluble, G is perfect, all the nonabelian composition factors of G are alternating groups.
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| first_indexed | 2025-11-29T12:10:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155198 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-29T12:10:31Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Cimetta, L. Lucchini, A. 2019-06-16T10:48:18Z 2019-06-16T10:48:18Z 2016 Normally ζ-reversible profinite groups / L. Cimetta, A. Lucchini // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 24-50. — Бібліогр.: 21 назв. — англ. 1726-3255 2010 MSC:20E07. https://nasplib.isofts.kiev.ua/handle/123456789/155198 We examine (finitely generated) profinite groups in which two formal Dirichlet series, the normal subgroup zeta function and the normal probabilistic zeta function, coincide; we call these groups normally ζ-reversible. We conjecture that these groups are pronilpotent and we prove this conjecture if G is a normally ζ-reversible satisfying one of the following properties: G is prosoluble, G is perfect, all the nonabelian composition factors of G are alternating groups. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Normally ζ-reversible profinite groups Article published earlier |
| spellingShingle | Normally ζ-reversible profinite groups Cimetta, L. Lucchini, A. |
| title | Normally ζ-reversible profinite groups |
| title_full | Normally ζ-reversible profinite groups |
| title_fullStr | Normally ζ-reversible profinite groups |
| title_full_unstemmed | Normally ζ-reversible profinite groups |
| title_short | Normally ζ-reversible profinite groups |
| title_sort | normally ζ-reversible profinite groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155198 |
| work_keys_str_mv | AT cimettal normallyζreversibleprofinitegroups AT lucchinia normallyζreversibleprofinitegroups |